Let's walk through the steps to find the expression that represents "the sum of a number and 9".
1. Understanding the Problem:
- We are given a phrase: "the sum of a number and 9."
- We need to translate this verbal phrase into an algebraic expression.
2. Identify Key Terms:
- "Sum" indicates addition.
- "A number" can be represented by a variable, commonly denoted by [tex]\( n \)[/tex].
3. Construct the Expression:
- We need to add the number [tex]\( n \)[/tex] and 9.
4. Forming the Algebraic Expression:
- To express this sum algebraically, you simply add the number [tex]\( n \)[/tex] and 9 together.
- This results in the expression [tex]\( n + 9 \)[/tex].
5. Choosing the Correct Option:
- Among the given options:
- [tex]\( n - 9 \)[/tex]: Represents the difference of a number and 9, not the sum.
- [tex]\( n + 9 \)[/tex]: Correctly represents the sum of a number and 9.
- [tex]\( 9n \)[/tex]: Represents the product of 9 and the number [tex]\( n \)[/tex], not the sum.
- [tex]\( \frac{n}{9} \)[/tex]: Represents the quotient of the number [tex]\( n \)[/tex] divided by 9, not the sum.
Therefore, the correct answer is:
[tex]\[
n + 9
\][/tex]
